The superfluid density is related to the phase stiffness, which is expressed as
\(\hbar ^{2}d\) /4\(\mu _{0}e^{2}\lambda _{\parallel }^{2}\) 
(\(d\) : interlayer distance) and yields approximately 4 K in \(\kappa \) -HgBr.
This value is considerably smaller than the values of the BCS case,
typically 10\(^{4}\) -10\(^{5}\)  K [1]}.
As the phase stiffness measures the macroscopic phase coherence in energy,
this small value in \(\kappa \) -HgBr is consistent with the previously observed field resilience and
strong fluctuations in superconductivity [2]}, [3]}.
From the penetration depth, the nominal Fermi temperature \(T_{\textrm {F}}\)  is
evaluated through the relation
\(k_{\textrm {B}}T_{\textrm {F}}\)  =
\(\pi \hbar ^{2}d\) /\(\mu _{0}e^{2}\lambda _{\parallel }^{2}\)  [4]}
to be approximately 45 K,
which gives a ratio, \(T_{\textrm {c}}/T_{\textrm {F}}\) , of \(\sim \) 0.09.
This is a large value beyond the BCS framework, where \(T_{\textrm {c}}\)  is
several orders of magnitude smaller than \(T_{\textrm {F}}\) . \(\kappa \) -HgBr is located in
the unconventional pairing region in the \(T_{\textrm {c}}\)  versus
\(T_{\textrm {F}}\)  plane (so-called Uemura plot), as shown in Fig. REF (c)
[4]}, [6]}, [7]}, [8]}.
